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Logicsmith Exhibition 3: Polyominous

Would you like to try your hand at logicsmithing, and possibly be featured on my blog? Read on!

In an intriguing experiment on its online puzzle site nikoli.com, the Japanese company Nikoli asked its authors to create different Slitherlink puzzles all using the same arrangement of givens. More recently, they asked its authors to create different Akari puzzles all using the same arrangement of black cells. I've decided to try a similar experiment here, using the puzzle Polyominous (link to rules, Polyominous puzzles from my blog). Your challenge is to replace each of the question marks in the grid below with an integer to create a uniquely solvable Polyominous puzzle.
Send your puzzle (and optionally, its solution) to my e-mail address at glmathgrant@gmail.com. After three weeks (meaning the deadline is September 7), I will post the puzzles that my readers and I have constructed for this layout. Good luck, and have fun!

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